# Calculus

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A hot air balloon rising vertically is tracked by an observer located 3 miles from the lift-off point. At a certain moment, the angle between the observer's line-of-sight and the horizontal is pi/5 , and it is changing at a rate of 0.1 rad/min. How fast is the balloon rising at this moment?

______ miles/min

• Calculus -

tanTheta=h/x

take derivative
sec^2 theta dtheta/dt= 1/x dh/dt

find dh/dt x= 3 miles theta= pi/5,dtheta/dt= .1rad/min

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